The Necker cube effect is a visual illusion wherein the mind constructs a cube from an image of a hexagon having a centre from which a line projects to each corner. In the illusion the centre alternatively projects towards or away from the observer.

The cube can be modelled as two interpenetrating mirror opposite tetrahedrons each having four corners a, b, c, d. The arrangement is such that the corners of the hexagon are ordered a, b, c, a, b, c.

The Necker cube effect models chiralkine counting better than a cube, because what appears to be the central “point” is always two points, one up and one down. In a cube the diagonals connecting the corners cross at one imaginary point, at which imaginary point opposed corners are one and the same. The features of the Necker cube are present independent of scale. The opposed corners and their behaviour as the Necker cube is “rotated” in space from one face to another are conserved no matter how small the Necker cube is shrunk.

The d in the diagram above, which represents the illusion of projection above or below the plane, is nothing other than the counterpart to one of the other three objects. This can best be appreciated by reviewing the page on how chiralkine counting works with particular reference to the drawing reproduced below.

The d’s in the centre of the Necker cube are the next of a, b and c to come into view to complete the fourth corner of a face. The system behaves like a fractal.